Kinetic description of avalanching systems

TL;DR

This paper introduces a kinetic framework for avalanching systems using cluster distribution functions, advancing beyond mean-field and renormalization approaches, with application to Earth's magnetosphere reconnection processes.

Contribution

It proposes a novel kinetic formalism for avalanching systems based on cluster distributions, providing deeper insight into their inhomogeneous structures.

Findings

Kinetic description captures cluster size distributions in avalanching systems.

Application to Earth's magnetosphere shows the model's relevance.

Advances understanding of inhomogeneous avalanching dynamics.

Abstract

Avalanching systems are treated analytically using the renormalization group (in the self-organized-criticality regime) or mean-field approximation, respectively. The latter describes the state in terms of the mean number of active and passive sites, without addressing the inhomogeneity in their distribution. This paper goes one step further by proposing a kinetic description of avalanching systems making use of the distribution function for clusters of active sites. We illustrate application of the kinetic formalism to a model proposed for the description of the avalanching processes in the reconnecting current sheet of the Earth magnetosphere.